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Os elementos estruturais, em muitas situações, estão apoiados em outros corpos, tais como o solo, que podem oferecer restrições de movimentos em algumas direções. Por isso, a análise estática e dinâmica desses elementos considerando sua interação com o solo torna-se importante na concepção de um projeto estrutural. Este artigo apresenta a análise dinâmica não linear de sistemas estruturais considerando tal interação através do Método dos Elementos Finitos. Um elemento de viga-coluna geometricamente não linear é usado para modelar a estrutura, enquanto o solo é idealizado como uma fundação contínua, através dos modelos de Winkler e Pasternak. Admite-se que a fundação reage aos esforços de tração e compressão, de modo que durante o processo de deformação os elementos estruturais são sujeitos a restrições de contato bilaterais. O método de integração de Newmark e a estratégia incremental-iterativa de Newton-Raphson são usados no processo de resolução das equações dinâmicas não lineares no domínio do tempo. Durante o estudo foram avaliadas situações práticas envolvendo a interação entre solo e estrutura, destacando a influência do contato nas frequências naturais de vibração e na resposta transiente dessas estruturas. Structural elements, in many situations, are supported by other surfaces, such as soil, which may offer movement constraints in some directions. Therefore, the static and dynamic analysis of these elements considering their interaction with the soil becomes important in the design of a structural design. This paper presents the nonlinear dynamic analysis of structural systems considering such interaction through the Finite Element Method. A geometrically nonlinear beam-column element is used to model the structure, while the soil can be idealized as a continuum foundation, through the Winkler and Pasternak models. It is assumed that the foundation reacts to tension and compression stresses, so during the deformation process the structural elements are subjected to bilateral contact constraints. The analysis is based on the modeling of the structural system using the finite element method, where the Newmark integration method and Newton-Raphson iterative strategy are used in the process of solving the nonlinear dynamic equations in the time domain. Practical situations involving the interaction between soil and structure were evaluated during the study, showing the influence of contact in the natural vibration frequency and transient response of these structures.

Structural elements, in many situations, are supported by other surfaces, such as soil, which may offer movement constraints in some directions. Therefore, the static and dynamic analysis of these elements considering their interaction with the soil becomes important in the design of a structural design. This paper presents the nonlinear dynamic analysis of structural systems considering such interaction through the Finite Element Method. A geometrically nonlinear beam-column element is used to model the structure, while the soil can be idealized as a continuum foundation, through the Winkler and Pasternak models. It is assumed that the foundation reacts to tension and compression stresses, so during the deformation process the structural elements are subjected to bilateral contact constraints. The analysis is based on the modeling of the structural system using the finite element method, where the Newmark integration method and Newton-Raphson iterative strategy are used in the process of solving the nonlinear dynamic equations in the time domain. Practical situations involving the interaction between soil and structure were evaluated during the study, showing the influence of contact in the natural vibration frequency and transient response of these structures.